The perturbative Ricci flow in gravity

TL;DR

This paper introduces a perturbative approach to Ricci flow in gravity, defining a renormalization scheme for Newton's constant and identifying a non-Gaussian fixed point through two-loop calculations.

Contribution

It develops a perturbative formulation of Ricci flow in gravity with flowed propagators and vertices, enabling renormalization group analysis of Newton's constant.

Findings

Derived counterterms for the flowed gravitational action.

Established a Ricci-flow based renormalization scheme for Newton's constant.

Identified a non-Gaussian fixed point consistent with non-perturbative results.

Abstract

We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton flow lines which describe the evolution of gravity along the Ricci flow. By calculating vacuum expectation values of a number of independent operators at the two-loop level, we derive the required counterterms of the flowed action. Our results allow us to define a Ricci-flow based renormalization scheme for Newton's constant $G_N$. Studying its renormalization group behavior, we recover a non-Gau{\ss}ian fixed point in accordance with well-known non-perturbative considerations